Collisional probability of planetesimals revolving in the solar gravitational field. II - The validity of the two-body approximation

Details Collisional probability of planetesimals revolving in the solar gravitational field. II - The validity of the two-body approximation Collisional probability of planetesimals revolving in the solar gravitational field. II - The validity of the two-body approximation

Sep 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989a%26a...221..342n&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 221, no. 2, Sept. 1989, p. 342-347.

Statistics

Computation

8

Computational Astrophysics, Gravitational Fields, Hill Method, Protoplanets, Solar Orbits, Two Body Problem, Collisions, Kepler Laws, Perturbation Theory, Planets, Planetesimals, Collisions, Gravity Fields, Two-Body Problem, Celestial Mechanics, Perturbations, Techniques, Calculations, Distance, Parameters, Theoretical Studies, Astronomy, Orbits

Scientific paper

We have investigated the validity of the two-body (free-space) approximation in the collisional problem between two Keplerian particles, i.e. two particles revolving in the solar gravitational field, by a perturbation method based on Hill's equation.
When the deviation of the nearest distance between two particles from that of the three-body problem is sufficiently small, we have found the radius rcr of the sphere of the two-body approximation, within which an orbit can be well described by a solution to the two-body problem. For the encounter between a protoplanet and a planetesimal, this rcr is given by
rcr=0.03(α0/1AU)-1-1/4(ξ/0.01)1/2hα0,
where α0 is the heliocentric distance of the protoplanet, hα0 its Hill radius and e the degree of deviation of the nearest distance. This result is very useful in numerically evaluating the collisional rate between Keplerian particles, which is essential for the study of the planetary accumulation; it enables us to stop the three-body numerical calculation at r = rcr and reduce the considerable computation time.

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